Show that the chemical potential at finite temperature given by
for the case kBT << µ. Useful result: When kBT
<< µ, the integral
reduces to
(Bethe-Sommerfeld expansion), where kBT = 1/?.
Show that the chemical potential at finite temperature given by for the case kBT << µ....
3. (a) The schematic temperature dependence of the chemical potential of CO2 is given below. Show how the melting pint (TT) will change when increase the pressure and justify your answer. Draw the new u-T line in the following scheme. (b) If this diagram is for water, repeat the same questions in (a). Solid Liquid Chemical potential, Gas Solid stable Liquid stable Gas stable Temperature, T
3. Consider a gas of fermion at a) Express the mean number of particle , and mean energy by polylogarithm function a) For a gas of fermion with density of state , show that the chemical potential is given by b) At finite temperature find the occupation number of the quantum state with energy . Explain qualitatively how this distribution would influence on the specific heat of the system. T7 0 We were unable to transcribe this imageWe were unable...
ChemActivity T10 Gibbs Energy as a Function of Temperature and Pressure 121 Model 2: Chemical Potential. For a pure phase, the chemical potential is given by where G is the molar Gibbs energy and n is the number of moles. Critical Thinking Questions 5. For a constant temperature process, what is the relationship between do, volume, and pressure? 6. A particularly useful relationship is that between G and volume and pressure for various systems at constant temperature. a) For condensed...
Consider a particle of mass in a 10 finite potential well of height V. the domain – a < x < a. a) Show that solutions for – a < x < a take the form on (x) = A cos(knx) for odd n, and on (x) = A sin(knx) for even n. . Show a) Match the boundary conditions at x = a to prove that cos(ka) = Bk where k is the wave vector for -a < x...
1. Consider the case where a liquid is confined between two walls a distance D apart with one wall located at r--D/2 and the other at x- D/2. The walls carry a surface charge density of ? and the liquid has only counter-ions to the surface charge. The Poisson-Boltzman equation (PBE) for this case is where is the electric potential that gives the electric field E- d '/dr, no is the nunber density of counter-ions of valency at x =...
Please make it simple and
clear to understand
3. A vector field is given by (a) Show that the vector field r is conservative. Then find a scalar potential function f(r,y,) such that r - gradf and f(0,0,0) 0 (b) By the result of (a) the following line integral is path independent. Using the scalar potential obtained in (a) evaluate the integral from (0,0,2) (where-y-0) to (4,2,3) (where -1,y 0,2) 4.2,3) J(0,0,2)
3. A vector field is given by (a)...
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Chemical potential/phases A substance has three phases: gas, liquid, and solid. The chemical potentials of various phases are illustrated below. T (K) 1) For a given temperature, which of the states represents an equilibrium condition? Submit 2) If the substance starts out in state Q and is held at constant temperature, what happens if it is allowed to reach equilibrium? The substance will freeze. The substance will evaporate The substance will melt and evaporate. The substance will sublime. Nothing...
Please show work step by step and
answer.
The Temperature Dependence of Chemical Equilibrium For an equilibrium reaction: - A+B Kc+o the following graph was obtained. 0.002 0.008 0.01 0.004 0.006 1/1 InK = -AHO + 4,50 Given the above relationship, use the graph to identify which of the following statements are "true" or "false" in this specific case. All statements refer to the forward reaction (proceeding left to right, as given) corresponding to the equilibrium constant K. The reaction...
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part...
(a) An experiment was conducted to analyze temperature distribution T(x) at a 2. distance x, measured from one side along a plate having length L. The result is given by the following function 1 where K = constant T(x) = Kx(1-x), 0 x Show that the Fourier sine series expansion representing T(x) is BKL 125 (55 marks)
(a) An experiment was conducted to analyze temperature distribution T(x) at a 2. distance x, measured from one side along a plate having...